热声现象的一种非线性模型的研究

本文对一种准一维非线性热声模型进行研究,利用该模型初步预测了一种热声驱动器的工作特性,并采用一种更简便的差分格式对系统中发生的非线性现象进行了数值模拟。结果表明,在频域内和线性条件下,该模型简化为经典的线性热声模型,可以预测热声驱动器的起振温度梯度;在时域内和非线性条件下,该模型可以模拟热声系统内的瞬态压力波由初始增长,经过非线性演化,最终达到饱和的全过程;最后,还讨论了板叠上的温度差对饱和压力波的影响。     

电磁迴旋不稳定性的准线性理论

在有弱相对论性电子时,在电子迴旋频率Ω_e附近存在快x模的不稳定性。从这一事实出发,我们用准线性理论分析了具有粒子数倒转的分布函数引起的不稳定性最后达到饱和的物理机制。进行了一些近似的计算,求出了电磁迴旋不稳定性的饱和时间和饱和能量及垂直、平行分布函数随时间的演化过程。发现用此理论算出的饱和能级与观察到的AKR结果是一致的。 关键词：     

Fourier-space nonlinear Rayleigh-Taylor growth measurements of 3D laser-imprinted modulations in planar targets

Nonlinear growth of 3D broadband nonuniformities was measured near saturation levels using x-ray radiography in planar foils accelerated by laser light. The initial target modulations were seeded by laser nonuniformities and later amplified during acceleration by Rayleigh-Taylor instability. The nonlinear saturation velocities are measured for the first time and are found to be in excellent agreement with Haan predictions. The measured growth of long-wavelength modes is consistent with enhanced, nonlinear, long-wavelength generation in ablatively driven targets.     

Self-organization of a plasma due to 3D evolution of the Weibel instability

The nonlinear evolution of the thermal Weibel instability is studied by using three-dimensional particle-in-cell simulations. After a fast saturation due to a reduction in the temperature anisotropy, the instability evolves to a quasistationary state which includes a single mode long wavelength helical magnetic field and a finite degree of temperature anisotropy. The nonlinear stability of this state is explained by periodic variations of the temperature anisotropy axis. At long time scales the magnetic field, wave number, and temperature anisotropy slowly evolve to the decreasing magnitudes.     

Nonlinear theory of resonant beam-plasma interaction: Nonrelativistic case

Analytic and numerical methods are used to study the nonlinear dynamics of the resonant interaction between a dense nonrelativistic electron beam and a plasma in a spatially bounded system. Regimes such as collective (Raman) and single-particle (Thomson) Cherenkov effects are considered. It is shown that in the first case, the motion of both the beam and plasma electrons exhibits significant nonlinearities. However, because of the weak coupling between the beam and the plasma, the nonlinear dynamics of the instability can be studied analytically and it can be strictly shown that saturation of instability is caused by a nonlinear shift of the radiation frequency and loss of resonance. In the second case, the nonlinear instability dynamics can only be studied numerically. In this regime, at low beam densities significant nonlinearity is only observed in the motion of the beam electrons while the plasma remains linear and saturation of the instability is caused by trapping of beam electrons in the field of the beam-excited plasma wave.     

Parametric Mechanism of Anomalous Microwave Power Absorption in Experiments on Electron Cyclotron Heating in Toroidal Magnetic Traps

The nonlinear stage of the parametric decay instability of an extraordinary wave is analyzed in the presence of a nonmonotonic density profile. The decay excites an electron Bernstein wave, which is localized in the vicinity of a local density maximum, and an ion Bernstein wave, which leaves a nonlinear interaction region and is absorbed by ions in the vicinity of the harmonics of the ion cyclotron frequency. The main mechanism of instability saturation is considered to be a cascade of decays of a primary daughter electron Bernstein wave, which leads to the excitation of localized secondary electron Bernstein waves and ion cyclotron (Bernstein) waves. The localization of electron Bernstein waves causes a significant decrease in the secondary- decay excitation threshold, which is thought to provide saturation of the primary instability at the lowest level. The saturation of the primary parametric decay instability of a pump wave and the anomalous absorption of the pump power are analytically estimated. A numerical simulation is performed using the parameters that are typical of the experiments on the electron cyclotron resonance heating of plasma at the second resonance harmonic in TCV tokamak.     

Nonlinear dynamics of filamentation instability and current filament merging in a high density current-driven plasma

The magnetic field generation due to the filamentation instability (FI) of a high density current-driven plasma is studied through a new nonlinear diffusion equation. This equation is obtained on the basis of quantum hydrodynamic model and numerically solved by applying the Crank–Nicolson method. The spatiotemporal evolution of the magnetic field and the electron density distribution exhibits the current filament merging as a nonlinear phase of the FI which is responsible for the strong magnetic fields in the current-driven plasmas. It is found that the general behaviour of the FI is the same as that of the classical case but the instability growth rate, its magnitude, and the saturation time are affected by the quantum effects. It is eventually concluded that the quantum effects can play a stabilizing role in such situation.     

Instability of moving gratings in photorefractive crystals

It is shown that a moving intensity grating in a photorefractive crystal with a sufficiently large lifetimemobility product can give rise to an instability against excitation of weakly damped space-charge waves. Increments and threshold of the instability are investigated for the threedimensional case. Subharmonics and other nonlinear scenarios of saturation are discussed.     

Nonlinear stage of development of resistive hose instability of a high-current relativistic electron beam in a plasma

The nonlinear stage in the development of a resistive hose instability of a highcurrent relativistic electron beam in a finite-conductivity plasma has been studied in the rigid-beam model. The attenuation of the force of the interaction of the beam with the magnetic field of the total current for large beam displacements is shown to result in the stabilization of the instability. The stabilization time and the amplitudes of the oscillations in the saturation regime are determined as functions of the parameters of the beam in the plasma.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fiz., No. 10, pp. 78–81, October, 1987.     

Nonlinear saturation amplitude of cylindrical Rayleigh Taylor instability

The nonlinear saturation amplitude （NSA） of the fundamental mode in the classical Rayleigh-Taylor instability with a cylindrical geometry for an arbitrary Atwood number is analytically investigated by considering the nonlinear corrections up to the third order. The analytic results indicate that the effects of the initial radius of the interface （r0） and the Atwood number （A） play an important role in the NSA of the fundamental mode. The NSA of the fundamental mode first increases gently and then decreases quickly with increasing A. For a given A, the smaller the ro/λ（λ is the perturbation wavelength）, the larger the NSA of the fundamental mode. When ro/λ is large enough （r0 〉〉 λ）, the NSA of the fundamental mode is reduced to the prediction in the previous literatures within the framework of the third-order perturbation theory.     

Saturation of backward stimulated scattering of a laser beam in the kinetic regime

Stimulated Raman (SRS) and Brillouin scattering (SBS) are examined in the kinetic regime using particle-in-cell simulations. Wave front bowing of electron-plasma waves (ion-acoustic waves) from trapped particle nonlinear frequency shift is observed in the SRS (SBS) regime for the first time. Self-focusing from trapped particle modulational instability (TPMI) is shown to occur in 2D and 3D SRS simulations. The key physics of SRS saturation is identified as a combination of wave front bowing, TPMI, and self-focusing: Bowing marks the beginning of SRS saturation and self-focusing terminates SRS. Ion-acoustic wave bowing also contributes to SBS saturation. Velocity diffusion by transverse modes and rapid loss of hot electrons in regions of small transverse extent formed from self-focusing dissipate wave energy and increase Landau damping, despite trapping that reduces Landau damping initially.     

X波段叠层片式微带铁氧体环行器的设计

采用叠层片式化设计有望实现微波环形器与低温共烧陶瓷(LTCC)技术的结合。借助三维电磁仿真手段设计了一种X波段微带铁氧体环行器,基片采用具有不同饱和磁化强度的旋磁材料构成叠层片式结构。研究结果表明,叠片数目及其饱和磁化强度的搭配对环形器的回波损耗和隔离度特性影响显著,这与叠层结构引入的界面及叠片变化的饱和磁化强度影响了环形器的等效输入电路参数有关。通过优化设计,可以获得具有高回波损耗、高隔离度及低插入损耗等优良性能的器件,但带宽受叠片数目及其饱和磁化强度的搭配影响较小,难以通过优化进行拓展。     

3/2omega0 radiation from the laser-driven two-plasmon decay instability in an inhomogeneous plasma

We present the results of the first reduced model simulations of the nonlinear development of the two-plasmon decay instability in an inhomogeneous plasma, including properties of the 3/2 harmonic emission. A sharp increase in radiation and Langmuir turbulence fluctuation levels occurs above a threshold laser intensity that depends on initial fluctuation levels. We study the competition between the linear propagation of Langmuir waves in the density gradient and the nonlinear saturation due to the Langmuir decay instability. The secondary decay Langmuir waves can provide the dominant source of the radiation and are essential to explain experiments.     

Multimode Coupling Theory for Kelvin-Helmholtz Instability in Incompressible Fluid

A weakly nonlinear model is proposed for multimode Kelvin-Helmholtz instability. The second-order mode coupling formula for Kelvin-Helmholtz instability in two-dimensional incompressible fluid is presented by expanding the perturbation velocity potential to second order. It is found that there is an important resonance in the course of the sum frequency mode coupling but the difference frequency mode coupling does not have. This resonance makes the sum frequency mode coupling process relatively complex. The sum frequency mode coupling is strongly dependent on time especially when the density of the two fluids is adjacent and the difference frequency mode coupling is not.     

Nonlinear theory of the ablative Rayleigh-Taylor instability

A fully nonlinear sharp-boundary model of the ablative Rayleigh-Taylor instability is derived and closed in a similar way to the self-consistent closure of the linear theory. It contains the stabilizing effect of ablation and accurately reproduces the results of 2D DRACO simulations. The single-mode saturation amplitude, bubble and spike evolutions in the nonlinear regimes, and the seeding of long-wavelength modes via mode coupling are determined and compared with the classical theory without ablation. Nonlinear stability above the linear cutoff is also predicted.     

Saturation of relativistic Weibel instability and the formation of stationary current sheets in collisionless plasma

We have studied the features of formation and the possible stationary structures of a self-consistent magnetic field in a relativistic collisionless plasma, which are characteristic of a simple geometry of the Weibel instability that is well known in the nonrelativistic case. The universal condition is established, the growth rate is determined, and the criteria of saturation of the Weibel instability are analyzed for a broad class of anisotropic particle distribution functions (for definiteness, in application to an electron-positron plasma). A nonlinear equation of the Grad-Shafranov type describing the potential current structures is derived and its solutions are analytically studied. Special attention is paid to spatially harmonic, nonlinear current configurations with parameters determined by the properties of the initial homogeneous plasma subject to the Weibel instability. It is demonstrated that the magnetic field energy density in the obtained solutions (both harmonic and nonharmonic) can be comparable with the kinetic energy density of plasma particles.     

Investigation on nonlinear thermo-acoustic characteristics of Rijke tube

Based on the energy conservation relationship,nonlinear thermo-acoustic effects of Rijke tube including instability range,saturation processes and higher harmonics modes were investigated.With coupling between the external flow and the inner space of a Rijke tube, the acoustic characteristics of self-excited oscillation were simulated.The experimental study was also carried out and the results were compared with those from simulation.The nonlinear factors which distort the acoustic waveform distortion were analyzed.From the results,it is seen that varying size of the nozzle outlet changes the acoustic impedance in the boundary, and leads to reduction of the nonlinear effects.The results show that the modes of self-excited oscillation could be influenced by the position of higher harmonics.In the large amplitude oscillation,the distortion of pressure wave within Rijke tube could be induced by the acoustic losses due to vortices on nozzle.It is found that the waveform distortion could be avoided by the shrinkage of nozzle.     

Intermittency at the onset of stochasticity in nonlinear resonant coupling processes

A simple model for the nonlinear saturation of a plasma instability is studied via numerical solution of the resonant three-wave coupling equations. When parameters are varied the attractors of motion undergo bifurcations of several types. Intermittency is shown to occur in a transition from a limit cycle to a strange attractor. Such a transition might be indicative of an intermittent onset of turbulence in certain plasma experiments.     

Increase of the backward Raman reflectivity caused by the langmuir decay instability in an inhomogeneous plasma: the loss of gradient stabilization

We investigate the nonlinear evolution of the backward stimulated Raman scattering (BSRS) in the regime where the nonlinear saturation mechanism is the Langmuir decay instability resulting from the coupling of the BSRS-generated Langmuir wave with the ion acoustic waves. We present numerical results obtained with a fluid-type code in one- and two-dimensional spatial dimensions, in the case of an inhomogeneous plasma. The plasma density is under quarter-critical and depends linearly on the longitudinal spatial coordinate, in the regime where the Rosenbluth gain factor for the amplitude, denoted as G(Ros), is in the range pi/2< or =G_(Ros)< or =6. We observe that the Langmuir decay instability is able to suppress the gradient stabilization and restore the absolute nature of BSRS, thus leading to a significantly increased BSRS reflectivity.